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We study the magic wavelength for two-photon 1 S – n S transitions in a hydrogen and deuterium atom, as well as 2 S – n S transitions, where the lower level is the metastable 2 S state. At the magic wavelength, the dynamic Stark shifts of the ground and the excited state of the transition coincide, so that the transition frequency is independent of the intensity of the trapping laser field. Experimentally feasible magic wavelengths of transitions with small slopes in the atomic polarizabilities are determined; these are the most stable magic wavelengths against variations of the laser frequency. We provide data for the magic wavelengths for the 1 S – n S and 2 S – n S transitions in hydrogen and deuterium, with n = 2 , ⋯ , 8 . We also analyze the stability of the elimination of the ac Stark shift at the magic wavelength against tiny variations of the trapping laser frequency from the magic value. [ABSTRACT FROM AUTHOR]